Evolution of the Solar Flare Energetic Electrons in the Inhomogeneous Inner Heliosphere

Solar flare accelerated electrons escaping into the interplanetary space and seen as type III solar radio bursts are often detected near the Earth. Using numerical simulations we consider the evolution of energetic electron spectrum in the inner heliosphere and near the Earth. The role of Langmuir wave generation, heliospheric plasma density fluctuations, and expansion of magnetic field lines on the electron peak flux and fluence spectra is studied to predict the electron properties as could be observed by Solar Orbiter and Solar Probe Plus. Considering various energy loss mechanisms we show that the substantial part of the initial energetic electron energy is lost via wave-plasma processes due to plasma inhomogeneity. For the parameters adopted, the results show that the electron spectra changes mostly at the distances before $\sim20 R_\odot$. Further into the heliosphere, the electron flux spectra of electrons forms a broken power-law relatively similar to what is observed at 1 AU.